is epistemic logic posible

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contextually definable in terms of 'know') occur essentially.1 The referenceto logical truth s he re has the purpose of requ iring epistem ic logic to begenuinely logic, while the referen ce to essen tial occ urren ces of epistemicter m s req uir es it to be genuinely epistem ic. It is, of c ours e, only logicalconstan ts that occur essen tially . Hence the effect of this definition, o the r-wise stated, is to make the question about epistemic logic equivalent to thequestion whether epistemic terms are ever logical constants.Th is definition not only requ ire s epistem ic logic to be both logic andabout knowing, as it should, but it also, as it should, gives us a criterion bywhich to distinguish ordin ary tru ths of logic from distinctive trut hs ofepistem ic logic. We need only look to see whether the epistem ic te rm soccur essentially as logical constants or whether they occur vacuously as,say, m ere p red icate s of pe rso ns . Thu s, the definition gives us a way todistinguish between:(a) Ifa knows that ft thenaknows thatp(Kapz> Kap)(b) If a knows thatp , thenp(KapDp)Both of the se may be admitted to be logical tru ths , but (a) is m erely aninstance of the ordinary logical truth "If qthen q containing two vacuousoccu rrences of the term 'know '. Of the two, only (b) (in which replacem entof 'knows that' by, say, 'believes that' would make (b) false of some personand some statement) can plausibly be counted a truth of epistemic logic. In(a), 'knows that' is a mere predicate ofa; only in (b) does it have any re-semblance to a logical constant.If (b) is an irred uc ible truth of epistem ic logic, then, of c ou rse , ou roriginal question must be answered affirmatively: he re is at lea st onedistinctive ep istem ic truth. And although we shall rais e some questionsnear the end about (b) let us admit that (b) is a convincing case, let it pass,and rev ise our original question accordingly, and it now becom es " A rethere any more such tru th s? " After all, one theorem doth not a system oflogic make.E. J. Lemmon, a pioneer in epistemic logic, comes very close to con-fessing that there a re not. He says [2, p. 78] "I t begins to look as though arealistic logic of knowing contains no distinctive theorems apart from (b)and its logical conseq uen ces." The reaso n it looks this way is that allcandidates for epistem ic theoremhood other than (b) have so far run afoul

1. An equivalen t definition could, of co ur se , be given by talking about the validityof ar gu m en ts. Th is definition is mode lled on Qu ine's famo us definition of' log ical t ru t h ' , [4 , p . 1 ] # A definit ion in fundamental re sp ec ts l ike Quine 's issketched by von Wright in [5]; Lemmon [2] seems content with the looser (andunexplicated) notion of "a na lyt ici ty" ; Hintikka evidently pre fe rs a definition inte rm s of " pos sib le w orld s" [3 , p . 41 ] , a no tion which i s no t on ly problemat icbut of which he ma kes a pec ulia r use . Unlike Leibniz, who req uir ed logic to betrue in al l pos sible w orld s, Hintikka is sat isfied if i t is t ru e in only one. Icannot h er e argu e the question of the nat ure of logical trut h, though, of cou rse ,everything depends on i t .


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of what Quine calls "referential opacity": they resist the extensionalityprinciple that truth functional equivalents are substitutable salva vertatae.Thus:(c) ( p q) (KapDKaq)is provable in most systems of epistemic logic. But suppose that "/>" is"Bugs Bunny is a rabbit" and q is "Bugs Bunny is an oryctolaguscuniculus. Then p Dq is true. Yet a man who knows rabbits but noLatin may know that p without knowing thatq: that is, Kap may be trueeven though Kaq is not.2

One is tempted to suppose that such situations (i.e. (c)) can be savedsimply by informing a of the fact that pz>q,the presupposition being thathe fails to know that qonly because he does not know that pDq. In otherwords, one is tempted to replace (c) by the weaker statement:(d) Ka(p Dq)D(Kap DKaq)But although an exception to (d) certainly seems less likely, it too is notwithout exception. Any supposition to the contrary fails to take account ofthe existence of what might be called Logically Obtuse Men (for short,LOMs), these being men who do not always deduce (come to know) whatobviously follows from what they do know. A LOM, for example, is anymanwho fails to recognize thatq,although he knows that p and although itis true that ifp thenq,thus violating the consequence of (c):(e) (Kap & ( / ) D q))DKaqOr, a LOM is the man who, by being "too stupid to put two and two together" f lsifies even so plausible a proposition as:(f) Ka(p&q)= (Kap&Kaq)

"Referential opacity" and "the Logically Obtuse Man" are but twolabels denoting the fact that there are knowers and knowledge constitutingcounterexamples to every extant theorem (provable result) of everyepistemic logic (excluding, of course (b)). The question of the possibilityof epistemic logic is whether there is any way to explain these counterexamples away. In what follows we shall examine attempts to do so byLemmonand vonWrightand, in much more detail, the attempts by Hintikka,whose book represents the most plausible and sustained effort yet toformulate, interpret, and defend an epistemic logic.3 We shall see that all

2. For a stricter definition of referential opacity, see Quine's [6].3. I shall not here treat Hintikka's quantification theory, to which the entireissue

of Nous, Vol. I, No. 1 is devoted. But I would make comparable objections.Roughly, in connection with quantification, referential opacity is marked byfailures of substitutivity of identities. Hintikka confesses on p. 52 of theNousissue however, that his treatment of quantification in epistemic contexts assumes: (x)(y)(x=y Ka(x=y))9But whether thisistrueispreciselythequestionat issue.


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these a ttem pts eit he r: (1) deny the co unterexamples by, in effect, makingthe term 'know' vacuous, o r (2) deny that epistem ic theo rem s need to bet rue. They there fore leave us with eithe r of two very urgent question s:(1) In what se nse is epistem ic logic epistemic? or (2) In what se nse is itlogic?2. Logically Perspicacious Knowers The epistemic logician's favoriteremedy for the malady we have labeled ' 'logical obtuseness" is a prescrip-tion originally concocted by Lemmon. It has been vario usly called the"rational man" or the "logically omniscient knower", but it shall here beknown as the L ogically Pe rsp icacious Knower (for sho rt, the LPK ). Unlikethe LOM, the LPK always lives up to the theorem s of epistemic logic.Why? Simply because he is the knower the epistemic logician has in mindwhen he formulates epistemic logic. Lemmon puts it this w ay: "We mustview ep istem ic logic as giving the logical tru ths concerning a logicalfiction, a so rt of 'ideal knower', the rational m an ", see [7]. Unfortunately,this med icine has unpleasant side e ffects. If e pistem ic logic is a logic ofLPK s alone, then it isn 't a logic for norm al men. It there fore ha sn'tanything to do with what we normally call "knowledge", a thing possessedby normal men who are not always as perspicacious as might be desired.It will be worthwhile to put this point more form ally. In effect,Lemmon is res tric ting the range of the variable name V in the exp ression6Kap9to L PK s. But since all of us m orta l humans ar e on occasion and tosome degree logically obtuse, this e limin ates actual know ers from therange of values of the personal variables in epistemic statements. Thusepistemic formulae have no interpretation in terms of, and are strictlymeaning less when applied to, actual kno wers. Hence Lemmon's qualifica-tion "realistic" and Hintikka's confession that "our results are notdirectly applicable to what is true or false in the actual world of ours.They tell us something definite about the truth and falsity of statementsonly in a world in which everybody follows the consequences of what heknows as far as they lead him" [3, p. 36].

The LPK thus exacts a grea t pr ic e. What is w orse, the epistem iclogician gets very little for his money. To be su re , by forbidding logic tobe about LOMs the epistem ic logician gua rantee s that the re ar e no beingsconcerning whom his theorem s are ever false. But since (saving God, andsurely we can leaveHim out of the question) there are no LPKs, he does soonly by making it doubtful whether there a re any beings of whom thesetheorems are ever true. Lemmon says that the LPK is a "fic tion ". Thefinal cost of the LPK, then, is the price of an ontology of fictions, a veryhigh price indeedN everth eless, let us suppose the price paid. What has been pu rchased ?So far we have preten ded that we would know an LPK if we met him . Butwhat ar e his distinguishing featu res? To ask this question is to re alizeimmediately that we know nothing about the LPK except that he is, by


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definition, the being of whom the theorems of epistemic logic are true. Butif that is so, to say that the theorems of epistemic logic are true of theLPK is merely to say that they are true of whomever they are true of: Wecan know whether we have bought the right medicine only after we havefound out whether it cures us.

Hintikka enlarges this circle a little, but not much. He defines theLPK as a being who knows all the "logical consequences of what he knows"(p .34). This means, from all appearances, merely that ifa knows thatp,an d if "# " is a logical consequence of "/>", thenaknows thatq, which isone of Hintikka's theorems (p. 30) and a special case of (e) above. Thus,to say that the LPK knows the logical consequences of what he knows ismerely to say that he is the person of whom (e) is true. Or, in general, tosay that the theorems of epistemic logic are true of the LPK is merely tosay that they are the theorems of epistemic logic.

We understand the LPK, therefore, only if we understand epistemiclogic, of which the LPK was supposed to make sense. Therefore we do notunderstand the LPK, except to this extent: whatever he may be, actuallyexisting knowers, being more orless logically obtuse, are not examples ofh i m . But the only sense of the word 'know which is familiar to us, isdefined precisely in terms of such actual knowers. We are therefore leftwith the question, In what sense of 'know does epistemic logic have anything to do with knowing?3. Knowledge andKnowledge2 As the most obvious way to respond to thefact that there are actual knowers who pose counterexamples to epistemiclogic is to answer that there are possible knowers who do not, so the mostobvious way to respond to the fact there is a sense of 'know for which itstheorems turn out to be false is to counter that there is a sense of 'knowfor which they do not. Von Wright, apparently the first to adopt this wayout,says "It is important to distinguish two interpretations of the phrase'it is known (verified) thata9, viz.i 'the proposition expressed byais known to be true (verified)', andii 'It is known (verified) thataexpresses a true proposition.'In this essaywe shall throughout understand the phrase 'it is known (verified) that ' in the interpretation i above." [1, p. 29] If the reader is notclear as to what distinction von Wright intends here, he can perhaps takesome comfort in the fact that there are at least two who are not clear. Butwe shall shortly return to this question.

Hintikka joins von Wright in this business of distinguishing two sensesof 'know. After announcing "By means of my rules it is readily seen thatKap DKaq is valid as soon as p logically implies q in our ordinarylogic" (p. 30), and then noting that there may be persons who know theaxioms of a mathematical system but not all its theorems (p. 31), Hintikkadistinguishes "active" from "virtual" knowledge (p. 34) and says that


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peoplealwaysvirtuallyknow the logical consequences of what they know althoughthey may notactivelyknow them.4

Making a distinction to resolve a contradiction is an old and respectable practice in philosophy. But it is not sufficient to make a distinction.I tis needed also to make it clear. The cryptic remark already quoted is,however, all that von Wright has to say by way of explanation of his distinct ion. His very next words are "As an undefined epistemic modality weintroduce the concept known to be true or verifiedafter which he proceeds to explain his symbols by givingus more symbols, scarcely pausingtonote that being genuinely epistemic would already be a way of being defined in terms of knowledge.5 Unfortunately, what is wanted is not formalelaboration but informal explanation. We need an interpretation of vonWright's epistemic modality, but this is precisely what von Wright does notsupply. Nor, as we shall see in greater detail later, does Hintikka do anybetterby virtual knowledge.

As a defense of epistemic logic this is, of course, circular. It merelysecures the theorems of epistemic logic by fiat: they are the truths aboutknowledge in the sence of 'know, whatever it may turn out to be, for whichthey are the truths about knowledge.

Itis, however, not really the circularity that is objectionable. What isobjectionable is the use of one unclear term to elucidate another uncleart e r m . We started out by trying to make sense of epistemic logic. We wereoffered knowledge and virtual knowledge. But if these have no definitionexcept in terms of epistemic logic then we do not understand them unlesswefirst understand epistemic logic: Thus we do not understand them.It should not be concluded from the preceding remarks that the dist inction von Wright and Hintikka intend does notexist. On the contrary, itcorresponds exactly to Quine's distinction between referentially opaque andreferentially transparent uses of the term 'know, which is roughly that at e rm Ka9 is used transparently in case the following is logically true andnot otherwise:(g) ip q) = (Kap=Kaq)Knowledge and virtual knowledge are, evidently, knowledge in the transp a r e n t sense. The difference, though it is considerable, is only that the4. H intikka also puts thisby saying that thereis a virtual implication between Kap and Kaq whenever p logicallyimp liesq, anexpression that seemstome tocommitsomanysins as to beho peless. Seenote6.5. Evidently, for a modal logician what makes modallogic to belogicis itspurelyformal features; what makes it to bemodal(i.e.alethic,epistemic, doxastic,

deontic, or whatever) is the particular interpretation to be assigned to the uninterpreted modal operator. The result is that modal logics areinterpreted formalisms, a notion I find parado xical. Th is paradoxis notgenerallynoted. Nor is thefact thatthecapacityforvariationofinterpretation (int e r m sof such diverse notions as ne cessity, knowledge,belief, obligationorwhatever)is very good evidence that themodal operator is not alogical constantofanykind.


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distinction is now made by re ference to truth functional logic, which isunproblematic and which we understand, whereas before it was made byrefe rence to epistem ic logic which is pro blem atic, and which we do notunderstand.Understood as knowledge in the transparent sense, then, the distinctionis cl ea r. Unfortunately, the epistem ic logicians cannot be pleased to haveit thus clarified. Fo r, first, they have proposed their distinction as a solu-tion to the problem of ep istem ic logic. But since that prob lem is pre cise lythe existence of referentially opaque uses of the term 'know' the putativesolutions amount merely to a restatement of the problem. Secondly, andmore seriously, the solution thus clarified constitutes an implicit reductionof epistem ic to ord inary truth functional logic. Fo r, in ess ence , to say thatthe 'Ka' of epistem ic logic is refe ren tially transpa ren t throughout is to saythat its presence makes no difference to the truth functionality of the con-texts in which it oc cu rs. This may p erhaps be made clear as follows: Callexpressions of the form 'Kap9, "epistemic sentences"; their parts 'Ka' andthe like, "epistemic operators", and their parts '/>' and the like, "proposi-tional co nte nts ". Then, using this purely schematic language, we may saythat the transparent epistemic operator is the one that makes no logical (inthe sense that it makes no truth-value) difference to the compounds inwhich it oc cu rs: That is , truth functionally speaking, the tran spare nt s enseof 'know' is the logically vacuous sense.

We therefore come to precisely the same conclusion as we reached inconnection with the LPK : epistem ic logic as a logic of virtual knowledge orknowledgei is simply logic in irrelev ant and misleading d re ss . This is notsu rp ris ing: the LPK was, of co urs e, simply any being who had knowledgein the transparent sense alone.4. Defensibility The LPK prese rve d the logical truth of the theore m s ofepistem ic logic by being that individual for whom, by stipulation, they weretru e. The notion of virtu al knowledge pr eserv ed the ir logical truth by beingthat sense of 'know' for which they w ere , again by stipulation, tru e. Bothstipulations were intended to preserve the logical truth of the theorems ofepistemic logic, and both did, although they managed this only by making itsrelev anc e to actual know ers and active knowledge prob lem atic, and byreducing epistem ic logic to logic. Hintikka, who enthus iastically end orse sboth notions, attemp ts there fore to supplement them by adding a uniquedefense and interp retatio n of epistem ic logic which is designed to se cu reits relevan ce to knowledge. Since the essence of this effort, how ever, is toreject the requirement that the theorems of epistemic logic be true, theres ult is m erely to pose the question "In what sense is 'epistem ic logic'logic?"

Hintikka begins his excellent and much discussed book by saying "Theword 'logi c' which occu rs in the subtitle of this w ork is to be taken se r -iously . My firs t aim is to formulate and to defend explicit cr ite ri a of con-sistency" (p. 31). He has no sooner begun to formulate these criteria thanhe begs leave to "r ei n te rp re t consistency as de fens ibility" (p. 31)although


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hedoesnotretracthisclaim that theterm 'logic' is to betaken seriously.Consistency has, of course, to dowith truth,andtherefore the terminological shift signalsthesurrenderof thenotionoftruth,asHintikkainforms usthattherulesof hisepistemic logic"are notconcerned withthetruth of statements at all;they merely tell us that certain adjunctionspreserve thedefensibility ofsets ofsentences." (p. 32)

T he causeof this terminological changeis thefact that thevery firsttheorem Hintikkaisabletoproveissimply false, andheknows it. Hesays"By means of myrules it is readily seen that KapDKaq is validassoon as p logically implies q in our ordinary propositional logic.6(Actually, what is provable in Hintikka's system is themuch strongerstatement(e) (Kap&(pDq))DKaq . But in onerespect this distinctiondoes notmatter: both thestronger and theweaker claim arefalse.) AsHintikka himself immediately recognizes, however, "it is clearly inadmissable toinfer 'heknows thatq9 from 'heknows that / > ' . . . for the person in question mayfail to seethatp entails q ; (Itwould be equallyinadmissable tomake theinference were we toreplace p entailsq byp Dq99.) Thus, inplace of theterm 'valid' (hisequivalent of 'logicallytrue') Hintikka uses theneologism 'self sustaining9. Theorems of epistemic logic are to becalled "self sustaining", which means that theirdenialsare, toemploy another neologismofHintikka's indefensible(p. 32).T h u s , to put itusing Hintikka's idiosyncratic "model set" language, theclaim that(e) is atheorem means thattheset7(h) { Kap ,p q, Kaq }(which, notice,iscomposedof the twoconjunctsof theantecedentof (e) andthedenialof (e)'sconsequent)is indefensible.86. Presumably H intikka means by p logically implies q , that pDq is atautology (logical truth), notm erely that "/> Z>q istrue. Itakeitthathewould express thelat ter bysaying simply p impliesq9f leaving theword' logically' out of it.Hisexpression pvirtuallyimpliesq99,Itherefore taketo

refer to aspecial epistemic logical relationwhichexistsbetweentwoespitemicstatements Kap and Kaq whenever"/> Dq is atautology. ButIam notatall sure that H intikkaisp erfectly scrupulousinobserving theuse mentiondistinction.7. I really havenotbeen abletodiscern anyconsistent principlegoverningHint ikka 'suse ofquotation marks . In thed escriptionofsets ,heusually quotestheepistemic statementsbut not theothers,apracticeIfollowhere .Butastatemen tin quotes isnamednotasserted, which raises the question whether namesofstatements,orstatements,orbothareelementsof model sets.*' Thisinturnraises a questionofinterpreting theclaim that m o d e l sets are inconsis

ten t or indefensible. Names of statements cannot beincom patiblewithstatementsorwithother namesofstatements.8. Amodel setformulation oftheclaim that "/>Z>p is atheorem wouldbethatth e set\p,/>}isinconsistent [3, p. 57],whichpresumably means thatthe conjunction p& p of itselementsis aco ntradiction.


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But what does 'indefensible' mean? To be sure, it is meant to be anepistemic analogue of 'inconsistent ', as 'self sustaining' is meant to be anepistemic analogue of 'valid'. But the analogy is not exact, and we reallyhave a better idea of what indefensibility is not than we have of what it is.We know only that, despite the evident analogy, 'indefensible' does not mean'inconsistent': (h) for example, is not inconsistent. On the contrary,Hintikka says that its elements may all be "simultaneously t rue" (p. 31).As Chisholm observes, "the sentences that Hintikka calls 'indefensible'may be true and, indeed may be known to be true" [7, p. 780], This, has, ofcourse, the paradoxical consequence that theorems of epistemic logic maybe false, a result which makes it especially important to understand what'indefensibility' does mean. U nfortunately, as Chisholm also observes, t h e author leaves this difficult question pretty much to the reader" [7,p . 780].

I t is true that Hintikka makes some effort to explain it. In fact, hemakes two efforts. One effort is to define defensibility as "immunity tocertain kinds of crit icism", an expression he endeavors to unpack bytalking about a person who is immune because he knows all the "logicalconsequences of what he knows" (p. 31) (or at least acknowledges themwhen they are pointed out to him).9 In short, one effort is to explicateindefensibility by invoking LPK's: indefensibility is inconsistency for LPKs(self sustenance is logical truth for an LPK). Another effort is to presentindefensibility as a property of denials that a person knows all the logicalconsequences "implicit" in what he knows. This makes indefensibility toconsist in denying that any man "virtually knows" all the logical consequencesof what he knows, or, as a wag might put it, it makes indefensibilityto consist in denying a theorem of epistemic logic. The two efforts, then,are to invoke the already discussed notions of the LPK and virtual knowledge. But if the notion of indefensibility is reducible to the LPK or tovirtual knowledge, we already know what objections are to be made to it.

Sensing that these two attempts are inadequate, Hintikka emulatesvon Wright and takes refuge in the formalities. Referring to his formalrules, he says: "The notion of defensibility is therefore exactly as intuitiveo r as precise as these rules. Any objections to my notions have to bedirected against them." (p. 34)

Letus ignore the familiar circularity which requires us to understandepistemic logic in order to understand the interpretation which is supposedto make sense of it for us. Let us, instead, take Hintikka's advice andexamine his rules.

Consider first, the pivotal rule which Hintikka calls (A.PK*), andwhich reads as follows:If a set of sentences is defensible and if Kapi e Kap2 e , ,Kapk e , Paq e , then the set{pl9 p2, .. .,pk9 q}is also defensible.

9. It seems likely that Hintikka has confused (e) "(#/>&(p q)) ~3Kaq with theverydifferent (weaker) proposition {Kapk*Ka{p^> q))D Kaq .


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T he expression 'Paqy, which we here encounter, is to be read: "it ispossible for all thataknows thatq. It is contexually defined by means ofanotherof Hintikka's rules as equivalent to'Kaq' which is to be read adoes not know that notq (p. 3 ff). If we henceforth include'Pa' in what wecall an "epistemic operator", then we may say that inspection of the rule(A.PK*) reveals it to be, in essence, an instruction to test the defensibilityof a set of epistemic sentences by inquiring (using normal truth functionalmeans which are made available by Hintikka's other rules) (p. 69) into theconsistency of the set's propositional contents, now bereft of their containing epistemic operators. The rule thus makes the entire logical interest inan epistemic set todevolve upon its propositional contents. In effect itsays "Throwawaythe troublesome operators 'Pa*and'Ka9 so that you canget to what matterslogically","where what matterslogically"are evidentlyth e'p9 andq\ The motivation for introducing the new expression 'Pa9 istofacilitate this process of getting at what is of logical interest by bringingthe negationsignsfrom outside an epistemic operator inside to bear on itspropositional contents. Thus, Chisholm remarks that Paq merely meansq is logically compatible with the set of all those sentencest such thataknows thattis true." [7, p. 779]

Hintikkaoffers two (though, hesays,provably equivalent) formulationsof his epistemic logic. One is by means of "rules" such as (A.PK*); theother is in terms of "conditions" for what he calls "alternative sets",alternative sets being sets of statements which representaas knowing "atleast as much as" he is represented as knowing in the sets to which theyare alternatives, (p. 52) This difference in formulation makes no differenceto the question at hand. If anything, the new formulation makes the pointclearer.

In the new formulation, conditions (C.KK*) and (C.P*) (see p. 70)jointly do the work of rule (A.PKK*), and determine a procedure thatHintikka calls a "reductive strategy" (p. 57). It is well named, being reductive in two senses: It proceeds by reducing knowledge claims to theirpropositional contents, and it is an epistemic version of reducto adabsurdum. On pages 5859 Hintikka uses it to prove (f) (Kap&Kaq) =Ka(p&q) . First he assumes that Kap , Kaq , and Ka(phq) areall members of a set . Then, using the definition of Kaq as Paq ,th eset is rewritten as{Kap , Kaq , Pa (p&q) }. Next an "alternative set", *, representing a "possible world" in whicha knows "atleast as much as he does in" , is formed by dropping, in accordance with(C.KK*), the'Ka'from the two left hand elements, and, in accordance with(C.P*) ,the'Pa9from the right hand element of the rewritten . The result,*, is the set {p, q(/>&q)},which is explicitly contradictory. Thus, bymeans of (C.P*) and (C.KK*), the original assumption thataknows thatp,and thatq,but does not know thatp &qhas yielded an explicit contradict ion . Hintikka claims that this procedure constitutes a proof that theoriginal set, , is indefensible, and therefore areductioadabsurdum proofthat (f) is selfsustaining (by definition of 'selfsustaining').

Clearly, thisproceduremakes theindefensibility of a set of epistemic


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sentences to consist in the inconsistency of their propositional contents.T he use of the conditions (C.KK*) and (C.P*) is merely to facilitate thediscovery of this contentual inconsistency. Clearly, also, this proceduremakes the selfsustenance of an epistemic theorem to consist in the factthat removal of its epistemic operators (sometimes after 6Kay operatorshave been judiciously replaced by Pay operators, or viceversa)yields at ruth functional tautology. For example, the above claim that (f) is selfsustaining amounts to no more than the claim that "(/>) D(p&q) is atautology, and the claim that (e) is a theorem amounts to the claim that(p &(pDq)) >q is a tautology. In short, a theorem of epistemic logic isany statement that turns out to be a theorem of truth functional logic whentheepistemic terms have been judiciously eliminated.

Indefensibility thus understood is clear, and so therefore is epistemiclogic. What is not clear is why anyone would suppose epistemic logic, thusunderstood, to be, in any significant sense, epistemic. It is merely logicapplied to the propositional contents of what happen to be knowledge claims.T he only explanation that comes to mind is that Hintikka confusesepistemic sentences with their propositional contents. For he uncriticallysupposes that if a set of contained propositions is logically objectionable,th eset of containing epistemic sentences is objectionable aswell. Indeed,th e assumption is thebasisof his "proof" procedure. Thus, in the proofoutlined above, the original set is said to be indefensible solelyon thegrounds that the alternative set * is inconsistent. This assumption, whichis plausible so long as the epistemic operators are all 'Ka' operatorswithout negation signs (it is not possible that Ka(p8 p), for example),loses all plausibility when'Pa' operators and denials of 'Ka' operators arein t roduced.

T he mistake is made explicit in Hintikka's informal commentary onthis "proof",which, hesays,is best thought of as "an abortive attempt todescribe consistently a state of affairs" in which someone knows thatpandknows thatq but does not know thatpandq (p. 58). But, there is no difficulty at all in consistently describing such a state of affairs; indeed it isnot too hard to discover an actual instance. The set { Kap , Kaq , Ka(p8z q) } is logically unobjectionable: What is objectionable is the set{p>Q> (P&SQ)}* In earlier pages, Hintikka was clearer that an indefensibleset may be composed of elements all of which are "simultaneously true."But unlike in earlier pages, he is not at this point worried about securingthetruthof his theorems. He is concernedsolelyto secure their relevancetoknowledge.

I t is this mistake which Chisholm means to bring out when he comm e n t s that Hintikka's term 'indefensible' is misleading, explaining that[7,p. 780 f]If I know that you do notaccept someof theconsequencesofsomeof thethings that you knowor that you believe somethingthatis logically false,and if I say as much, thenmytrue sentenceis 'indefensible*. Ordinarily,however,we should say that what is indefensibleinsuchasituationis notmyown sentence,or statementof it (questionsof etiquette aside),butwhat


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itis thatI amdescribing, namely your neglecttodrawall theconsequencesofwhatyouknow,oryour acceptanceof somethingthatis logically false.This is exactly right, and it is devastating, although Chisholm himself doesnotseem to realize how decisive a blow he has struck. Chisholm adds that'shocking', 'disappointing', and the like would be less misleading terms.N otso: if adoes not know all the logical consequences of what he knows,an dif I say so, it is still notmystatement but 's stupidity which is "disappointing", "shocking", "scandalous", or whatever.

Confusion so deepwillnot be soeasily eradicated. The question is notth e choice of condemnatory words, but what is to be condemned by meansof those words? The painful fact is that confusion as to the proper subjectof epistemic logical predicates is fundamental to Hintikka's "proof"procedures. Wanting to appraise not merely propositional contents butepistemic statements, he condemns descriptions of failures of knowledgewhen it is only the failures of knowledge that can be condemned. This isexactly analogous to accusingJones of asserting a contradiction because hehas reported (by, perhaps quoting Smith) that Smith has uttered one. Inshort, Hintikka's "proof" procedure requires systematic commission ofth eusemention fallacy.

T hepreceding argument ignores Hintikka's rule (A.PKK*), of which hewould surely remind us, and which reads as follows:If a set of sentences is defensible and if Kapx e , Kap2 e , . . . , Kapk e , Paq e , thenthe set{ Kapu Kap 2, . . . , K apk, q] isalso defensible.According to Hintikka, "the applicability of (A.PKK*) as distinguished from(A.PK*) presupposes that a statement of the form " knows thatp can becriticized not only by discussing whether pis true, but also by discussingwhether the bearer of the termais in a position or condition really to knowit." (p. 18)10 If, then, there are any distinctive, irreducible epistemict h e o r e m s , they are theorems whose proofs essentially involve the rule(A.PKK*).Hintikkaproves one such theorem, the Reiteration Theorem (RT):(i) KapDKaKapStraightforwardly interpreted, the RT expresses the Cartesian doctrine ofthe self illumination of the knowing mind, according to which any man whoknows something also knows that he knows it. But Hintikka's RT cannot bestraightforwardly interpreted. A person can,Hintikka admits, both knowsomething and also fail to recognize that he knows it.11 Thus the RT doesnotmean that the set

10. Note thetacit confession that (A.PK*) makes thequestion whetherKapto consistin thequestion whetherp.11. See pp. 117 ff. N evertheless H intikka talks in ChapterIV asthough KaKapwerealogicalconsequenceof Kap .


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(j) { Kap, KaKap }is inconsistent. It means only that (j) is indefensible.

But what does that mean? We have thus far been able to make senseo u t of Hintikka's notion of indefensibility by interpreting it as the inconsistency of propositional contents. That interpretation is no longer available to us. If it were, then the claim that set (j) and its equivalent set{ Kap, PaKap } areindefensible would amount to the claim that the set{p, Kap } is inconsistentwhich would be tantamount to the claim thatp DKap ("Everything true is known bya or a is.omniscient") is selfsustaining. Not only is this absurd (though it is very agreeable to havelogic assure one of omniscience), but it cannot have been intended byHintikka.12 For then the whole of epistemic logic, including (A.PKK*),would reduce to ordinary truth functional logic. The application of(A.PKK*), like (A.PK*), would "presuppose" only that p is true.

'Indefensibility' cannot, therefore, (nor can Hintikka want it to) meanth e same thing in connection with (A.PKK*) and the RT, as it does in conn e c t i o n with (A.PK*) and the ET. Hintikka himself unembarrassedly makesthis point when he says that there is no one interpretation of 'defensible' or'know' whichwill satisfy both (A.PK*) and (A.PKK*), it being necessary tointerpret the term one way in connection with the one and another way inc o n n e c t i o n with the other. (A.PKK*) is designed to express a "primary"sense of the word 'know' while (A.PK*) captures a "secondary" sense(p . 19, ff).

But if this is so, the fundamental terms of Hintikka's epistemic logicare equivocal, and his epistemic logic fails to reduce to logic pure andsimple when (A.PKK*) is added only because he has violated the fundamental rule of good logical practice: have distinct symbols for distinctlogical concepts. Hintikka has an embarrassment of riches: not one, buttwo epistemic logics. Of one of these we have so far made some sense. Itis the one which deals with 'know' in the secondary sense, which, for thet r u t h of Kap , presupposes only the truth of "/>", and which is, therefore,equivalent to ordinary truth functional logic. Of the other we have yet tomake any sense. Perhaps we may do better in the next section.5. Epistemic Logic and Performatives On the assumption that logic hasessentially to do with truth and falsity, we have pretended that Hintikka'sepistemic logic must have been intended as a logic of statements, a statem e n t being definable as the sort of thing of which 'ture' or 'false' can bepredicated. But the decision to replace 'inconsistent' by 'indefensible' andth e consequent announcement that epistemic logic "tells us nothing aboutt r u t h and falsity" means that it is not meant to be a logic of statementsafter all. On the contrary, Hintikka says that it is meant as a logic of"sentences" whose rules "merely tell us that certain adjunctions alwayspreserve the defensibility of sets of sentences." (p. 32)

12. Hintikka comes close, however, to proving an omniscience theorem on p. 79,where hesaysthat it isepistemically indefensible to say li & Kap .


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If we employ the old but honorable distinction between the act ofasserting something and thesomething thereby asserted, calling the formera "sentence" and latter a "statement", we shall have a rough idea of whatH i n t ik k a means by the distinction. For Hintikka, a sentence is an act ofmaking a statement; the statement is what is made. Indefensibility is aproperty, not of the statement made, but of the making of it. It is a pointwhich Hintikka also puts by sayingthat indefensibility is "of a performatoryc h a r a c t e r (p. 77), using Austin's term to refer to the performance of"uttering". Thus, when he says "If you want to see in the equivalence [ofKap with KaKap ] a more interesting truth [than Cartesianism], youmay try the quasi performatory character of l know' statements rathert h a n the transparency of our minds" (p. I ll) , he means, to quote Chisholm,t h a t the RT says "not that knowing in any sense implies knowing that oneknows; it is rather that if a man does not know that he knows . . . then heshouldn'tsay that he knows."

Previously we wondered how a true statement could be objectionable.N o w we have a partial answer: it is not the statement but the act of makingit that is objectionable. This answer is, however, only partial. We can allunderstand that there may be nothing wrong with what is said even whent h e r e is something wrong with saying it. One must not, for example,r min an ugly woman of her affliction. But as Chisholm also observes,H i n t ik k a is not discussing tact. He claims to be talking logic [7, p. 786 f.].

T o account for his insistence on this point, we must realize thatH i n t ik k a is speaking, not merely of speech acts, but of speech acts in thefirst person. His paradigm case is the person who claims in one breath toknow thatp and in the other not to know that he knows it, (and, we shall see,t h e person who says "I know thatp, p Dq,but I do not know that # ") . Inpedestrian parlence, such a person would be accused of "contradictinghimself."13 Hintikka's epistemic logic is a monument to his conviction thatthis usage embodies sound logical intuitions.

H e realizes, however, that such statements are not, by ordinarycriteria of logic, "inconsistent". For suppose the person in question is a.T h e na having said:(k) Kip & KiKip( w h e r e K i p = I k n o w t h at / ? ) h a s s a id :(1) Kap KaKap.But (1) may, as Hintikka freely acknowledges, be true, it being entirelypossible for a to know something and not yet to have realized selfconsciously that he does. Therefore, since a =i, (k) may also be true. Butwhat can be true cannot be inconsistent. Therefore, neither (k) nor (1) isinconsistent.

H i s loyalties thus divided between plain talk and plain logic, he grasps

3 See Hintikka's Section (4.5) ff for thebasisof the following remarks.


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thehorns and resolves his dilemma by saying that the above are objectionableas sentences though notasstatements, indefensible though not inconsistent. Here Hintikka correctly uses 'statement' to refer to somethingindependent of speaker, and incorrectly uses 'sentence' to refer to something that is not (he should have used 'sentence token'), and his point is thatwhat is objectionable is for a to say (k), and therefore (1),abouthimself.Someoneelse, say b (b a),could assert (1) abouta,but cannot assert (1)abouthimself,because, by so doing, he would be asserting (k). The difference,in short, lies wholly on the side of the speaker and in his speech act.

This limitation to the first person is a point on which it is easy to bemisled. Since the first person pronoun makes statement dependence explicit, one might think that Hintikka ought to formulate his results by usingth e first person pronoun. Instead, he throughout uses the impersonalvariable name ' ' in deliberate preference to the personal pronoun ' , andhe vigorously insists that his results are not valid merely for the "firstperson singular pronoun" (p. 68). Nevertheless, they are valid merely forthe first person. Hintikka is capitalizing on the fact that there are twomodes of first person reference. Ve may call them Plebian first personan d Royal first person. Plebian first person makes use of the personalpronoun ' , and is a first personmode of first person reference. Royalfirst person is a third person mode of first person reference, it being away of referring to oneself by, say, the use of one's own name or title.Hintikka, who wishes not only to condemn "I know thatpbut do not knowthat I know it" but also "Jones knows thatp but does not know that heknows it" as saidby Jones, formulates his results by using ' ' ratherthan ' . This giveshis epistemic logic an appearance of generality whichit does not in fact enjoy. For Royal and Plebian first person are equallyfirst person references, different only in the manner in which they accomplish reference. Hintikka's epistemic logic is thus an impersonal logic toabout the same degree as, considering the loop holes, the U.S. graduatedincometax is a burden on the rich.

Hintikka is himself aware of this restriction to first person when(A.PKK*) and the RT are concerned. On p. 22 he does note that (A.PKK*)is to be applied only to cases where the speaker "knows that he himself isbeing referred to", and, in a footnote, he says, dropping the reference topronouns , that it would be impossible to generalize his results beyond thefirst person (p. 74). He never explicitly places a comparable restriction on(A.PK*) and theorems such as (Kap&(pDq))DKaq) , butitis a limitation which would make them considerably more plausible than they haveheretofore seemed and would also integrate (A.PK*) and (A.PKK*) into thesame system of logic, and avoid the charge of equivocation. According tovulgar idiom, it is also "self contradictory" to deny knowing what oneexpressly acknowledges to follow from what one claims one does know.

I t follows that epistemic logic, interpreted as a set of criteria forassessingacts of advancing first person knowledge claims, is a much morerestricted thing than it might seem, and consists of much weaker claimsthan one might think. This weakness is, however, also a strength. For, so


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interpreted, epistemic logic is a very plausible thing indeed. There issomething wrong with (k). The question is, What? Or rather, the questionis whether its defect islogical.By way of explanation of what he claims is logically wrong with saying(k),Hintikka refers us to his discussion of Moore's problem about:(m ) pbut I do not believe thatp.This,he says,violates "the general presumption that the speaker believeswhat hesays," (p. 67) and therefore, by uttering it, "the speaker giveshishearers all they need to overthrow" it; it is "selfdefeating", "indefensiblefor the speaker to utter" (p. 72). Indefensible sentences, then, are "selfdefeating" speech acts by means of which the speaker "overthrows" whathesays about himself in the very act of saying it. So far, so good, but wemust now explain the explanation, and in particular the metaphor "overthrow".Oneplausible explanation is that, in normal circumstances, 's sayingp is justification enough to conclude thatabelieves thatp. Our criterionfor whether a person believes something is usually simply that hesays it.In normal circumstances, saying is believing. Of course, there is thepossibility of insincerity, which, if it occurs,will defeat our criterion andupset this pretty equation. But supposeais sincere in saying p . Thenour criterion applies and he believes thatp. Thus when he adds that hedoes not believe thatp,hesays what is condemnable asfalse. Suppose, onth e other hand, that he is not sincere when he says p and does not believe thatp. Then his act is condemnable as insincere. Ineither case,something is condemnable. Hence something is condemnable.

T hecase of saying (1) Kap &KaKap is similar. Asserting the firstconjunct "gives rise to the presumption that" the second conjunct is true.We not only expect people to believe what they assert; we expect them to"know what they are talking about." Thus, ifa says (k), he is condemnableeitherfor not knowing what he is talking about (when hesays that he knowstha t p),or for saying what is false (when he adds that he does not know thatheknows it), but in either case, he is condemnable.

This makes good sense. But if this is all there is to epistemic logic,epistemic logic consists merely of such maxims as: (1) Be sincere;(2) Know what you are talking about; and (3)Alwaystell the truth. All areexcellent maxims to which no one can take exception. But the questionremains: What have they to do with logic? Insincerity is a defect ofmorals; not knowing what you are talking about is a defect of character orupbringing; and making false statements (that are not lies) is caused byignorance.

Nevertheless, Hintikka is convinced that being a selfdefeating act is aspecifically logical defect (p. 65). Why? The answer seems to be that, likewhat are called "analytic" statements, selfdefeating speech acts are notmerely condemnable, buteasily seento be condemnable. Somewhat as onecan impeach "some bachelors are married" by examining a minimal number of bachelors, so one can impeach Jones' assertion of (m) without


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IS EPISTEM IC LOGIC POSSIBLE? 449

independent inquiry into Jones' beliefs: for if Jones said it sincerely, it isfalse; and if it is true, thenhe said it insincerely.

This, however, only makes an already loose notion of analyticity a gooddeal looser. No doubt, it is gravely objectionable to say what any fool cansee to be false. But it is time to recognize (as Hintikka himself suspectswhen he pretends that what he has been doing by means of his "reductivestrategy" is deriving contradictions) that there is really only one objectionfrom logic to any speech act: that by means of it the speaker makes astatement which is logically false. Theact is objectionable because thestatement is, and otherwise it is not. The explanation of indefensibility interms of selfdefeat in speech acts thus makes epistemic logic plausiblewithout making it logic.

There remains, however, one other interpretation of Hintikka's remarkthat indefensibility is "of a performatory character" which does make itlogic. Hintikka, we may remember, uses the term 'performative', asAustin later apparently came to use 'illocutionary act', to mean simply thespeech performance. In Austin's "Other Minds" [8] the term carries moreweight. When Austin says there that 'I know in "I know thatp is a performative, he seems to mean two things, one negative and one positive. Thenegative, and really important point, is that "I know thatp isautobiographically or descriptively vacuous,saying nothing about the speaker andgrammatical subject. Thus Austin says "To suppose that know is adescriptive phrase is only one example of the descriptive fallacy socommon to philosophy." The positive point is that 'I know, although notessential in adescriptive way, is nevertheless essential to aperformancewhich can be compared to warrantying what one is claiming to know. ThusAustin says "When I say know, Igive others my word: Igiveothers myauthorityfor sayingthat S is P ." (See also [9].)

In this discussion, Austin seems to use the word 'descriptive' to meanwhat we have here meant by 'statement' so that the joint effect of negativean d positive sides of his thesis is that I know that p is statementally{descriptively) equivalentwith p . Ordinarily we might suppose that "Iknow thatp is equivalent with the conjunction of p and some statementabout,say, the speaker's state of mind. But Austin seems to be challengingthis assumption and advancing in its place a redundancy theory of knowledge whichsays that the t ruthvalue of "I know t h a t / ? is the same as thatof p and that the two differ only performatively.

Let us suppose that Austin's account as thus interpreted is correct.Then Kip is t ruth functionally equivalent to p (as is Kap whenaistalking). This has somevery interesting consequences for epistemic logic.T he most interesting is that the Epistemic Theorem and ReiterationT h e o r e m bothturnout to be nothing more than cumbersome and misleadingformulations of the tautology p z>p ( Kap being equivalent to p , andKaKap being equivalent to Kap ) with extraneous and irrelevant epistemic operators tacked on, and needing, by means of Hintikka's rules, tobe pulled off before any evaluation is possible. This suggests that Hintikka's logic may be, in a sense even Hintikka perhaps does not suspect, a


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logic of know in its performative use.14 For suppose one were to goaboutconstructing a "logic of knowing" according to Austin's account. Tworules would become central, one expressing the descriptive vacuity, theother the performative essentiality of know. The first would allowdropping off epistemic operators because they make no difference, and thesecond would permit adding them on because, since they can then bedropped, they make no difference. In other words, the first would beHintikka's rule (A.PK*) and the second would be his (A.PKK*). One's logicwould also have two corresponding theorems: Kap Dp and KapDKaKap , the Epistemic and Reiteration Theorems. In short, one wouldhave Hintikka's epistemic logic.

But notice that the essence of such an epistemic logic is thatit isepistemic in a descriptively vacuous sense of the term 'know*. It istherefore simply logic. The theorems of epistemic logic are just so manydisguised tautologies. The Reiteration Theorem, for example, is simplyth e tautology pz>p , and the theorem "(Kap &(pDq))DKaq is thetautology (p &(pDq))Dq . Not even Lemmon's apparent exception, theEpistemic Theorem escapes this reduction.

We have, then, two different interpretations of Hintikka's remark thatepistemic logic is a logic of performatives. Jointly these interpretationsyield the now familiar dilemma: either epistemic logic concerns selfdefeating speech acts and has, perhaps, something to do with knowledge butnothingto do with logic, or else it concerns a performative use of 'know,which, because it is descriptively vacuous has plenty to do with logic butnothingessentially to do with knowing.6. Epistemic Logic as Normative Science Epistemic logic a la Hintikkawas to avoid invalidation by counterexamples by being a logic of defensibility rather than a logic of truth, and was to manage this by being a logicof speech acts rather than statements. As we have seen, the plausibility ofsuch a logic, which is considerable when it is restricted to speech acts inth e first person, may be due simply to the fact that the acts of saying pan d"I know thatp make the same statement, viz. "/>", so that a personcannot affirm one and deny the other without thereby uttering a strictlyself contradictory statement. In short, the plausibility of such a "logic"may verywellbe that it is just logic after all.

There remains one last interpretation of epistemic logic which construes it as having nothing essentially to do with statements and truth.According to this interpretation, epistemic logic is anormative science,telling us not what people in fact know but rather what theyought to know,given that they know something else.

N o epistemic logician has yet explicitly endorsed such an interpret a t ion , 15 but Hintikka's term 'indefensibility' certainly has normative14. See Max Deutscher's review of Hintikka, [10], Allan White in his review [11]

also notes that Hintikka is trying to formulate a logic of speech acts.1 5 . But also see pp. 37 f of Hintikka's book.


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conno tations. So does Lemmon's LPK, which is m ost plausibly construedas an ideal worthy of emulation by LOM s. Fu rthe rm ore , such an in ter pr e-tation has undeniable appeal. Pro fessionally comm itted as he is tologicality and rationality, every logician is a sort of priest of the LPK forwhom failure to be logical is the graves t of sin s. He cannot deny, forexample, that he thinks it indefensible to fail to know (or acknowledge)16 allthat follows from what one does know (or claim s to know), more esp ec iallywhen it is pointed out to him.But if the logician cannot deny the appeal of a norm ative interp reta tionof epistemic logic, he can wonder what se nse it m akes. Norm ative notionsare , after all, notoriously difficult to analyze, and are philosophically moreproblem atic than descriptive notions. Can we really expect to clarify com-paratively unproblematic talk about what is the case by means of obscureand problematic talk about whatoughtto be the ca se?H istorically, normative inte rpretatio ns of logic were a reaction tonineteenth century psychologism , which took prin ciple s of logic to be de -scriptions of the necessities of thought, and so concluded that no one could"th in k" co ntradictions. The normative interpretation agreed that logic hasto do with thought, but cautioned that it prescribes norms for correctthought and does not describe the actual processes, which may be quiteillogical. This was quite an improvem ent.It still is . Epistem ic logic construed as co nsisting of d escriptivestatements about the necessities of actually existing knowledge is merelyfalse, and is much more palatably construed as determining a set of canonsfor logically consistent knowledge.Improvem ent though it is over psycho logism, however, any norm ativeinterpreta tion of logic still suffers from thre e defects. Fi rs t, the inter pr e-tation needs inte rpr etin g. Second, it turns things around: one shouldn't"think" a contradiction because it would be illogical to do so; a contradic-tion isn 't illogical because one shouldn't think it. Th ird, the norm ativeinterpretation is itself at least quasi-psychologistic, unless interpreted asP eir ce interp reted it. As Pe irc e saw [12], to say that logic is a normativescience of thought is to say, in a misleading way, that it really hasn't any-thing to do with thought as such, but that it ha s, rat he r, to do with truth ,truth being already norm ative for thought (for prag m atic rea sons ): if youought to "think" the conclusion of an argument, it is solely because itspr em ise s a re tru e and the argument is valid. From the normative int er-pretation, therefore, we get no clarification but only connotations of theirrelevant.7. Summary and Conclusions We have cons idered two ways, and twovariations on each way, in which epistemic logic has been defended againstthe charge that its theorems are not logical truths about knowing orkno wers. The first way is to counter that ther e is a sense of 'know' for16. Actually, epistemic logic is much more plausibly construed as a logic ofacknowledgments than as a logic ofknowledge.


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which they are logical truths; or that there are knowers who never presentcounterexamples. The second way is to deny that they need to be true, andtopresent them instead as criteria for the assessment of defensible speechacts, or as norms for knowledge. Which defense the epistemic logicianelects seems to depend on whether he is, at the time, concerned to defendepistemic logic against the charge that it isn't true or against the chargetha tit isn't about knowing.

We have seen that the first defense saves epistemic logic from thecharge of falsehood only because the sense of 'know for which its theoremsaretrue is the logically vacuous transparent sense, and only because thereareno logically perfect knowers for the theorems of epistemic logic to betrue of. We have seen that the second defense at first glance makes itdoubtful whether epistemic logic is logic, since logic in that sense whichhas governed our discussion consists precisely of logical truths. But wehave also seen that this defense too ultimately borrows what plausibility itpossesses from the fact that it is merely a defense of logic in epistemicdisguise. Presented as a set of criteria for defensible speech acts,epistemic logic makes sense only if these are criteria assessing thestatemental contents of those speech acts. Its cash value as a normativescience consists in the fact that logic, pure and simple, is alreadynormative for knowledge.

N ot having examined all possible ways of defending epistemic logicwhich may occur to the fertile brains of epistemic logicians, we cannotclaim to have seen that there can be no such thing as epistemic logic.Nevertheless, we have seen enough to make it look as if the failure ofepistemiclogic is no accident but is inherent in the nature of the case. If itis to deserve the epithet 'epistemic', epistemic logic needs a logicallyessential use of the term 'know, but if it is to deserve the encomium'logic' it also evidently needs a sense of the term that makes no logicaldifference. A term that makes no logical difference is, however, scarcelya logically essential term. What the epistemic logician wants is for theterm 'know to be botha logical constant and an ordinary predicate ofpersons,but he can't have t ha t .

Wereit not for the Epistemic Theorem, Kap Dp it seems likelythatthe dubiousness of the rest of the putative theorems of epistemic logicwould long ago have caused it to be consigned to the garbage heap of discarded philosophical ideas. If epistemic terms are descriptively vacuous,as Austin contends, the Epistemic Theorem is equivalent to p Dp , andrequires no special consideration. But if epistemic terms are descriptivelyvacuous, thenthe evidentlyfalse converse of the Epistemic Theorem, viz.,p K ap , the Omniscience Theorem, would also be equivalent to thetautology p Dp".

The case of the Omniscience Theorem perhaps has a solution in a"semantical theory of knowledge" similar to a semantical theory of t r u t h .Or, more likely perhaps, Austin is only partially right and there areuses of 'know that are descriptively vacuous but also uses that arenot . If so, it seems likely that the Epistemic Theorem may be aninstance of thefirst, and the Omniscience Theorem an instance of the


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lat ter . It may be,thatis, that whenwe are talking about knowledge,we aresometimes talking about what-is-known (and this is the case in theEpistemic Theorem)and that we are sometimes talking abouttheknowing(and this is evidently the case in the Omniscience Theorem),andthatwecan havea logicofknowingin thefirst, but not in the second case.There is an old but honorable distinction between the act of knowingandthecontent whichis relevant here. The word 'knowledge'is ambiguousreferring sometimes to the act and sometimes to the content. If we askwhether there can be a logic of knowledge, we are therefore askingtwoquestions. The resultof this paper is that theanswer to the one is yesandthe answer to the other is no . Thereis no doubt thatwe can havealogicofcontentsofknow ledge. Infactwe already have sucha logic, thoughit contains no epistemic operators. But it appears that there can be nologic of knowledge in the sense that there can be a logic of the actsofknowing. In short,we can have a logic of what weknow (which, how ever,t reats the fact that we know it as irrelevant); but it appears thatwe canhavenologicof theknowing.

R F R N S

[1 ] von Wright, G. H., " E p i s t e m i c M o d a l i t i e s / ' An Essay in Modal Logic, NorthHolland Publishing Co.,Am ster da m (1951).[2] Lemmon, E. J. , If I know do I know that Iknow" inE pistemology, ed. byAvrum Stro l l , Harper and Row, NewYork (1967).

[3] Hintikka, Jaak ko, Knowledge and Belief Cornell (1967).[4] Quine,W. V.,Mathematical Logic, H a r p e r and Row, NewYork (1965).[5 ] von Wright, G. H., " F o r m andcontent inl o g i c , " inLogical Studies, Routledgeand Kegan Paul (1957).[6] Quine, W. V., "Reference and modal i ty " inFrom a Logical Point of View,Harvard, Cambridge (1953).[7] Chisholm, R. M., The logic of knowing," The Journal ofP hilosophy, 60(1963),p.773-795.[8] Austin, J. L., " O t h e r m i n d s , " inPhilosophical Papers, Oxford (1961).[9] Danto, Arthur C., On knowing thatweknow," inE pistemology, ed. by AvrumStro l l , Harper and Row, New York (1967).

[10] Deutscher, Max,Review ofKnowledge and Belief Mind 75 (1966),pp.145-149.[11] White, Allan, Review of Knowledge and Belief Philosophical Quarterly, 15(1965),pp.268-269.[12] Pei rce, C. S., Collected Papers, Volume V,Ha rvard Pr e ss (1934), parag raph365.

UniversityofAlabamaUniversity, Alabama

is epistemic logic posible

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